- #1

DryRun

Gold Member

- 838

- 4

**Homework Statement**

Using Green's theorem, evaluate:

http://s2.ipicture.ru/uploads/20120117/6p57O2HO.jpg

**The attempt at a solution**

[tex]\frac{\partial P}{\partial y}=3x+2y[/tex]

[tex]\frac{\partial Q}{\partial x}=2y+10x[/tex]

[tex]\frac{\partial Q}{\partial x}-\frac{\partial P}{\partial y}=7x[/tex]

To do the integration, i'm using the parametric equations of the circle; x= cosθ and y=sinθ

[tex]\int\int 7\cos \theta \,.rdrd\theta[/tex]

The curve C is a circle with centre (1,-2) and radius r=1

I've drawn the graph in my copybook.

Description of circle:

For θ fixed, r varies from r=-2 to r=-3

θ varies from -∏/2 to -∏/2

However, i can't get the correct answer as i'm quite sure that i've got the wrong limits. Usually, i deal with circles with centre (0,0) so it's easier to find the limits for r and θ.